I will assume you want to publish DITA content using a Jenkins server. If you want something else, please provide us with more details.Oxygen uses for publishing DITA content an engine called the DITA Open Toolkit which can also be downloaded and invoked separately (on the server side):

I understand and I stick to my previous answer.Using Jenkins you can start any process on the server side. So on the server side you can have a Jenkins job which first downloads the current DITA content for the documentation from your CMS or version control system, then downloads a DITA Open Toolkit (from the DITA OT website I mentioned), unzips it, then runs the DITA OT process specifying various parameters to it (path to the DITA Map, output format). Then the Jenkins job can take the output content and move it to a web server to publish it.